%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWC100+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:41:35 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC100+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 07:58:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.41 fof(f4,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> ( singletonP(U)<=> (? [V] :( ssItem(V)& cons(V,nil) = U ) )) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f5,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( frontsegP(U,V)<=> (? [W] :( ssList(W)& app(V,W) = U ) )) ) )) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f6,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( rearsegP(U,V)<=> (? [W] :( ssList(W)& app(W,V) = U ) )) ) )) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f7,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( segmentP(U,V)<=> (? [W] :( ssList(W)& (? [X] :( ssList(X)& app(app(W,V),X) = U ) )) )) ) )) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f15,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( neq(U,V)<=> U != V ) ) )) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f16,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> (! [V] :( ssItem(V)=> ssList(cons(V,U)) ) )) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f17,axiom,(
% 0.13/0.41 ssList(nil) ),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f28,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> app(nil,U) = U ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f41,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> ( ( frontsegP(U,V)& frontsegP(V,U) )=> U = V ) ) )) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f45,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> frontsegP(U,nil) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f51,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> rearsegP(U,nil) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f57,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> segmentP(U,nil) ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f84,axiom,(
% 0.13/0.41 (! [U] :( ssList(U)=> app(U,nil) = U ) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f96,conjecture,(
% 0.13/0.41 (! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ strictorderedP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssItem(X2)& (? [X3] :( ssList(X3)& app(X3,cons(X2,nil)) = W& lt(X2,Z) ) )) )) )) )) ))| ( nil != X& nil = W )| ( ( nil != V| nil = U )& ( ~ neq(V,nil)| ( neq(U,nil)& frontsegP(V,U) ) ) ) ) ) )) )) )) )),
% 0.13/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.41 fof(f97,negated_conjecture,(
% 0.13/0.41 ~((! [U] :( ssList(U)=> (! [V] :( ssList(V)=> (! [W] :( ssList(W)=> (! [X] :( ssList(X)=> ( V != X| U != W| (! [Y] :( ssList(Y)=> ( app(W,Y) != X| ~ strictorderedP(W)| (? [Z] :( ssItem(Z)& (? [X1] :( ssList(X1)& app(cons(Z,nil),X1) = Y& (? [X2] :( ssItem(X2)& (? [X3] :( ssList(X3)& app(X3,cons(X2,nil)) = W& lt(X2,Z) ) )) )) )) )) ))| ( nil != X& nil = W )| ( ( nil != V| nil = U )& ( ~ neq(V,nil)| ( neq(U,nil)& frontsegP(V,U) ) ) ) ) ) )) )) )) ))),
% 0.13/0.41 inference(negated_conjecture,[status(cth)],[f96])).
% 0.13/0.41 fof(f113,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(singletonP(U)<=>(?[V]: (ssItem(V)&cons(V,nil)=U))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.13/0.41 fof(f114,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|((~singletonP(U)|(?[V]: (ssItem(V)&cons(V,nil)=U)))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f113])).
% 0.13/0.41 fof(f115,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|((~singletonP(U)|(ssItem(sK4_skl(U))&cons(sK4_skl(U),nil)=U))&(singletonP(U)|(![V]: (~ssItem(V)|~cons(V,nil)=U)))))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114])).
% 0.13/0.41 fof(f118,plain,(
% 0.13/0.41 ![X0,X1]: (~ssList(X0)|singletonP(X0)|~ssItem(X1)|~cons(X1,nil)=X0)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f115])).
% 0.13/0.41 fof(f119,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(frontsegP(U,V)<=>(?[W]: (ssList(W)&app(V,W)=U))))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 0.13/0.41 fof(f120,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|(?[W]: (ssList(W)&app(V,W)=U)))&(frontsegP(U,V)|(![W]: (~ssList(W)|~app(V,W)=U)))))))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f119])).
% 0.13/0.41 fof(f121,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|(ssList(sK5_skl(V,U))&app(V,sK5_skl(V,U))=U))&(frontsegP(U,V)|(![W]: (~ssList(W)|~app(V,W)=U)))))))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120])).
% 0.13/0.41 fof(f123,plain,(
% 0.13/0.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|app(X1,sK5_skl(X1,X0))=X0)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f121])).
% 0.13/0.41 fof(f124,plain,(
% 0.13/0.41 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|frontsegP(X0,X1)|~ssList(X2)|~app(X1,X2)=X0)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f121])).
% 0.13/0.41 fof(f125,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(rearsegP(U,V)<=>(?[W]: (ssList(W)&app(W,V)=U))))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.13/0.41 fof(f126,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~rearsegP(U,V)|(?[W]: (ssList(W)&app(W,V)=U)))&(rearsegP(U,V)|(![W]: (~ssList(W)|~app(W,V)=U)))))))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f125])).
% 0.13/0.41 fof(f127,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~rearsegP(U,V)|(ssList(sK6_skl(V,U))&app(sK6_skl(V,U),V)=U))&(rearsegP(U,V)|(![W]: (~ssList(W)|~app(W,V)=U)))))))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126])).
% 0.13/0.41 fof(f129,plain,(
% 0.13/0.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~rearsegP(X0,X1)|app(sK6_skl(X1,X0),X1)=X0)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f127])).
% 0.13/0.41 fof(f130,plain,(
% 0.13/0.41 ![X0,X1,X2]: (~ssList(X0)|~ssList(X1)|rearsegP(X0,X1)|~ssList(X2)|~app(X2,X1)=X0)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f127])).
% 0.13/0.41 fof(f131,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(segmentP(U,V)<=>(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U))))))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.13/0.41 fof(f132,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~segmentP(U,V)|(?[W]: (ssList(W)&(?[X]: (ssList(X)&app(app(W,V),X)=U)))))&(segmentP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(app(W,V),X)=U)))))))))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f131])).
% 0.13/0.41 fof(f133,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~segmentP(U,V)|(ssList(sK7_skl(V,U))&(ssList(sK8_skl(V,U))&app(app(sK7_skl(V,U),V),sK8_skl(V,U))=U)))&(segmentP(U,V)|(![W]: (~ssList(W)|(![X]: (~ssList(X)|~app(app(W,V),X)=U)))))))))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132])).
% 0.13/0.41 fof(f136,plain,(
% 0.13/0.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~segmentP(X0,X1)|app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0))=X0)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f133])).
% 0.13/0.41 fof(f137,plain,(
% 0.13/0.41 ![X0,X1,X2,X3]: (~ssList(X0)|~ssList(X1)|segmentP(X0,X1)|~ssList(X2)|~ssList(X3)|~app(app(X2,X1),X3)=X0)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f133])).
% 0.13/0.41 fof(f217,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|(neq(U,V)<=>~U=V))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.13/0.41 fof(f218,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~neq(U,V)|~U=V)&(neq(U,V)|U=V)))))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f217])).
% 0.13/0.41 fof(f219,plain,(
% 0.13/0.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~neq(X0,X1)|~X0=X1)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f218])).
% 0.13/0.41 fof(f220,plain,(
% 0.13/0.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|neq(X0,X1)|X0=X1)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f218])).
% 0.13/0.41 fof(f221,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssItem(V)|ssList(cons(V,U)))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.13/0.41 fof(f222,plain,(
% 0.13/0.41 ![X0,X1]: (~ssList(X0)|~ssItem(X1)|ssList(cons(X1,X0)))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f221])).
% 0.13/0.41 fof(f223,plain,(
% 0.13/0.41 ssList(nil)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f17])).
% 0.13/0.41 fof(f248,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|app(nil,U)=U)),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.13/0.41 fof(f249,plain,(
% 0.13/0.41 ![X0]: (~ssList(X0)|app(nil,X0)=X0)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f248])).
% 0.13/0.41 fof(f283,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|(![V]: (~ssList(V)|((~frontsegP(U,V)|~frontsegP(V,U))|U=V))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f41])).
% 0.13/0.41 fof(f284,plain,(
% 0.13/0.41 ![X0,X1]: (~ssList(X0)|~ssList(X1)|~frontsegP(X0,X1)|~frontsegP(X1,X0)|X0=X1)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f283])).
% 0.13/0.41 fof(f294,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|frontsegP(U,nil))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 0.13/0.41 fof(f295,plain,(
% 0.13/0.41 ![X0]: (~ssList(X0)|frontsegP(X0,nil))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f294])).
% 0.13/0.41 fof(f308,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|rearsegP(U,nil))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f51])).
% 0.13/0.41 fof(f309,plain,(
% 0.13/0.41 ![X0]: (~ssList(X0)|rearsegP(X0,nil))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f308])).
% 0.13/0.41 fof(f322,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|segmentP(U,nil))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f57])).
% 0.13/0.41 fof(f323,plain,(
% 0.13/0.41 ![X0]: (~ssList(X0)|segmentP(X0,nil))),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f322])).
% 0.13/0.41 fof(f388,plain,(
% 0.13/0.41 ![U]: (~ssList(U)|app(U,nil)=U)),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f84])).
% 0.13/0.41 fof(f389,plain,(
% 0.13/0.41 ![X0]: (~ssList(X0)|app(X0,nil)=X0)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f388])).
% 0.13/0.41 fof(f415,plain,(
% 0.13/0.41 (?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&strictorderedP(W))&(![Z]: (~ssItem(Z)|(![X1]: ((~ssList(X1)|~app(cons(Z,nil),X1)=Y)|(![X2]: (~ssItem(X2)|(![X3]: ((~ssList(X3)|~app(X3,cons(X2,nil))=W)|~lt(X2,Z)))))))))))))&(nil=X|~nil=W))&((nil=V&~nil=U)|(neq(V,nil)&(~neq(U,nil)|~frontsegP(V,U)))))))))))))),
% 0.13/0.41 inference(pre_NNF_transformation,[status(thm)],[f97])).
% 0.13/0.41 fof(f416,definition,(
% 0.13/0.41 ![U,V]: (sP0_prd(V,U)<=>(nil=V&~nil=U))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.13/0.41 fof(f417,plain,(
% 0.13/0.41 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&strictorderedP(W))&(![Z]: (~ssItem(Z)|(![X1]: ((~ssList(X1)|~app(cons(Z,nil),X1)=Y)|(![X2]: (~ssItem(X2)|(![X3]: ((~ssList(X3)|~app(X3,cons(X2,nil))=W)|~lt(X2,Z)))))))))))))&(nil=X|~nil=W))&(sP0_prd(V,U)|(neq(V,nil)&(~neq(U,nil)|~frontsegP(V,U))))))))))))),
% 0.13/0.41 inference(formula_renaming,[status(thm)],[f415,f416])).
% 0.13/0.41 fof(f418,plain,(
% 0.13/0.41 ?[U]: (ssList(U)&(?[V]: (ssList(V)&(?[W]: (ssList(W)&(?[X]: (ssList(X)&((((V=X&U=W)&(?[Y]: (ssList(Y)&((app(W,Y)=X&strictorderedP(W))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=Y))|(![X2]: (~ssItem(X2)|((![X3]: (~ssList(X3)|~app(X3,cons(X2,nil))=W))|~lt(X2,Z)))))))))))&(nil=X|~nil=W))&(sP0_prd(V,U)|(neq(V,nil)&(~neq(U,nil)|~frontsegP(V,U))))))))))))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f417])).
% 0.13/0.41 fof(f419,plain,(
% 0.13/0.41 (ssList(sK47_skl)&(ssList(sK48_skl)&(ssList(sK49_skl)&(ssList(sK50_skl)&((((sK48_skl=sK50_skl&sK47_skl=sK49_skl)&(ssList(sK51_skl)&((app(sK49_skl,sK51_skl)=sK50_skl&strictorderedP(sK49_skl))&(![Z]: (~ssItem(Z)|((![X1]: (~ssList(X1)|~app(cons(Z,nil),X1)=sK51_skl))|(![X2]: (~ssItem(X2)|((![X3]: (~ssList(X3)|~app(X3,cons(X2,nil))=sK49_skl))|~lt(X2,Z))))))))))&(nil=sK50_skl|~nil=sK49_skl))&(sP0_prd(sK48_skl,sK47_skl)|(neq(sK48_skl,nil)&(~neq(sK47_skl,nil)|~frontsegP(sK48_skl,sK47_skl)))))))))),
% 0.13/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f418])).
% 0.13/0.41 fof(f420,plain,(
% 0.13/0.41 ssList(sK47_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.13/0.41 fof(f423,plain,(
% 0.13/0.41 ssList(sK50_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.13/0.41 fof(f424,plain,(
% 0.13/0.41 sK48_skl=sK50_skl),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.13/0.41 fof(f425,plain,(
% 0.13/0.41 sK47_skl=sK49_skl),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.13/0.41 fof(f426,plain,(
% 0.13/0.41 ssList(sK51_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.13/0.41 fof(f427,plain,(
% 0.13/0.41 app(sK49_skl,sK51_skl)=sK50_skl),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.13/0.41 fof(f430,plain,(
% 0.13/0.41 nil=sK50_skl|~nil=sK49_skl),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.13/0.41 fof(f431,plain,(
% 0.13/0.41 sP0_prd(sK48_skl,sK47_skl)|neq(sK48_skl,nil)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.13/0.41 fof(f432,plain,(
% 0.13/0.41 sP0_prd(sK48_skl,sK47_skl)|~neq(sK47_skl,nil)|~frontsegP(sK48_skl,sK47_skl)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f419])).
% 0.13/0.41 fof(f433,plain,(
% 0.13/0.41 ![U,V]: ((~sP0_prd(V,U)|(nil=V&~nil=U))&(sP0_prd(V,U)|(~nil=V|nil=U)))),
% 0.13/0.41 inference(NNF_transformation,[status(thm)],[f416])).
% 0.13/0.41 fof(f434,plain,(
% 0.13/0.41 (![U,V]: (~sP0_prd(V,U)|(nil=V&~nil=U)))&(![U,V]: (sP0_prd(V,U)|(~nil=V|nil=U)))),
% 0.13/0.41 inference(miniscoping,[status(thm)],[f433])).
% 0.13/0.41 fof(f435,plain,(
% 0.13/0.41 ![X0,X1]: (~sP0_prd(X0,X1)|nil=X0)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f434])).
% 0.13/0.41 fof(f436,plain,(
% 0.13/0.41 ![X0,X1]: (~sP0_prd(X0,X1)|~nil=X1)),
% 0.13/0.41 inference(cnf_transformation,[status(thm)],[f434])).
% 0.13/0.41 fof(f438,definition,(
% 0.13/0.41 sQ0_spl <=> (nil=sK50_skl)),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f439,plain,(
% 0.13/0.41 nil=sK50_skl|~sQ0_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f438])).
% 0.13/0.41 fof(f441,definition,(
% 0.13/0.41 sQ1_spl <=> (nil=sK49_skl)),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f443,plain,(
% 0.13/0.41 ~nil=sK49_skl|sQ1_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f441])).
% 0.13/0.41 fof(f444,plain,(
% 0.13/0.41 sQ0_spl|~sQ1_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f430,f438,f441])).
% 0.13/0.41 fof(f445,definition,(
% 0.13/0.41 sQ2_spl <=> (sP0_prd(sK48_skl,sK47_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f446,plain,(
% 0.13/0.41 sP0_prd(sK48_skl,sK47_skl)|~sQ2_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f445])).
% 0.13/0.41 fof(f448,definition,(
% 0.13/0.41 sQ3_spl <=> (neq(sK48_skl,nil))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f449,plain,(
% 0.13/0.41 neq(sK48_skl,nil)|~sQ3_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f448])).
% 0.13/0.41 fof(f451,plain,(
% 0.13/0.41 sQ2_spl|sQ3_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f431,f445,f448])).
% 0.13/0.41 fof(f452,definition,(
% 0.13/0.41 sQ4_spl <=> (neq(sK47_skl,nil))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f454,plain,(
% 0.13/0.41 ~neq(sK47_skl,nil)|sQ4_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f452])).
% 0.13/0.41 fof(f455,definition,(
% 0.13/0.41 sQ5_spl <=> (frontsegP(sK48_skl,sK47_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f457,plain,(
% 0.13/0.41 ~frontsegP(sK48_skl,sK47_skl)|sQ5_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f455])).
% 0.13/0.41 fof(f458,plain,(
% 0.13/0.41 sQ2_spl|~sQ4_spl|~sQ5_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f432,f445,f452,f455])).
% 0.13/0.41 fof(f462,plain,(
% 0.13/0.41 ![X0]: (~ssList(cons(X0,nil))|singletonP(cons(X0,nil))|~ssItem(X0))),
% 0.13/0.41 inference(destructive_equality_resolution,[status(thm)],[f118])).
% 0.13/0.41 fof(f463,plain,(
% 0.13/0.41 ![X0,X1]: (~ssList(app(X0,X1))|~ssList(X0)|frontsegP(app(X0,X1),X0)|~ssList(X1))),
% 0.13/0.41 inference(destructive_equality_resolution,[status(thm)],[f124])).
% 0.13/0.41 fof(f464,plain,(
% 0.13/0.41 ![X0,X1]: (~ssList(app(X0,X1))|~ssList(X1)|rearsegP(app(X0,X1),X1)|~ssList(X0))),
% 0.13/0.41 inference(destructive_equality_resolution,[status(thm)],[f130])).
% 0.13/0.41 fof(f465,plain,(
% 0.13/0.41 ![X0,X1,X2]: (~ssList(app(app(X0,X1),X2))|~ssList(X1)|segmentP(app(app(X0,X1),X2),X1)|~ssList(X0)|~ssList(X2))),
% 0.13/0.41 inference(destructive_equality_resolution,[status(thm)],[f137])).
% 0.13/0.41 fof(f474,plain,(
% 0.13/0.41 ![X1]: (~ssList(X1)|~ssList(X1)|~neq(X1,X1))),
% 0.13/0.41 inference(destructive_equality_resolution,[status(thm)],[f219])).
% 0.13/0.41 fof(f475,plain,(
% 0.13/0.41 ![X0]: (~ssList(X0)|~neq(X0,X0))),
% 0.13/0.41 inference(duplicate_literals_removal,[status(thm)],[f474])).
% 0.13/0.41 fof(f489,plain,(
% 0.13/0.41 ![X0]: (~sP0_prd(X0,nil))),
% 0.13/0.41 inference(destructive_equality_resolution,[status(thm)],[f436])).
% 0.13/0.41 fof(f498,plain,(
% 0.13/0.41 sK48_skl=nil|~sQ0_spl),
% 0.13/0.41 inference(backward_demodulation,[status(thm)],[f439,f424])).
% 0.13/0.41 fof(f500,plain,(
% 0.13/0.41 app(sK47_skl,sK51_skl)=sK50_skl),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f425,f427])).
% 0.13/0.41 fof(f504,definition,(
% 0.13/0.41 sQ6_spl <=> (ssList(nil))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f506,plain,(
% 0.13/0.41 ~ssList(nil)|sQ6_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f504])).
% 0.13/0.41 fof(f507,definition,(
% 0.13/0.41 sQ7_spl <=> (ssList(sK47_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f509,plain,(
% 0.13/0.41 ~ssList(sK47_skl)|sQ7_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f507])).
% 0.13/0.41 fof(f510,definition,(
% 0.13/0.41 sQ8_spl <=> (frontsegP(app(sK47_skl,sK51_skl),sK47_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f511,plain,(
% 0.13/0.41 frontsegP(app(sK47_skl,sK51_skl),sK47_skl)|~sQ8_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f510])).
% 0.13/0.41 fof(f513,definition,(
% 0.13/0.41 sQ9_spl <=> (ssList(sK51_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f515,plain,(
% 0.13/0.41 ~ssList(sK51_skl)|sQ9_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f513])).
% 0.13/0.41 fof(f517,plain,(
% 0.13/0.41 ~nil=sK47_skl|sQ1_spl),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f425,f443])).
% 0.13/0.41 fof(f518,plain,(
% 0.13/0.41 $false|sQ9_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f515,f426])).
% 0.13/0.41 fof(f519,plain,(
% 0.13/0.41 sQ9_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f518])).
% 0.13/0.41 fof(f520,plain,(
% 0.13/0.41 sP0_prd(sK50_skl,sK47_skl)|~sQ2_spl),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f424,f446])).
% 0.13/0.41 fof(f521,plain,(
% 0.13/0.41 nil=sK50_skl|~sQ2_spl),
% 0.13/0.41 inference(resolution,[status(thm)],[f435,f520])).
% 0.13/0.41 fof(f522,plain,(
% 0.13/0.41 sP0_prd(nil,sK47_skl)|~sQ2_spl),
% 0.13/0.41 inference(backward_demodulation,[status(thm)],[f521,f520])).
% 0.13/0.41 fof(f569,plain,(
% 0.13/0.41 ![X0]: (singletonP(cons(X0,nil))|~ssItem(X0)|~ssList(nil)|~ssItem(X0))),
% 0.13/0.41 inference(resolution,[status(thm)],[f462,f222])).
% 0.13/0.41 fof(f570,definition,(
% 0.13/0.41 ![X0]: (sQ16_spl <=> (singletonP(cons(X0,nil))|~ssItem(X0)|~ssItem(X0)))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f573,plain,(
% 0.13/0.41 sQ16_spl|~sQ6_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f569,f570,f504])).
% 0.13/0.41 fof(f574,plain,(
% 0.13/0.41 $false|sQ6_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f506,f223])).
% 0.13/0.41 fof(f575,plain,(
% 0.13/0.41 sQ6_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f574])).
% 0.13/0.41 fof(f577,plain,(
% 0.13/0.41 $false|sQ7_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f509,f420])).
% 0.13/0.41 fof(f578,plain,(
% 0.13/0.41 sQ7_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f577])).
% 0.13/0.41 fof(f579,plain,(
% 0.13/0.41 ![X0]: (~ssList(X0)|~ssList(nil)|app(nil,sK5_skl(nil,X0))=X0|~ssList(X0))),
% 0.13/0.41 inference(resolution,[status(thm)],[f123,f295])).
% 0.13/0.41 fof(f581,definition,(
% 0.13/0.41 ![X0]: (sQ17_spl <=> (~ssList(X0)|app(nil,sK5_skl(nil,X0))=X0|~ssList(X0)))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f584,plain,(
% 0.13/0.41 sQ17_spl|~sQ6_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f579,f581,f504])).
% 0.13/0.41 fof(f587,plain,(
% 0.13/0.41 app(sK47_skl,sK51_skl)=nil|~sQ2_spl),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f521,f500])).
% 0.13/0.41 fof(f593,plain,(
% 0.13/0.41 frontsegP(nil,sK47_skl)|~sQ2_spl|~sQ8_spl),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f587,f511])).
% 0.13/0.41 fof(f601,plain,(
% 0.13/0.41 neq(nil,nil)|~sQ0_spl|~sQ3_spl),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f498,f449])).
% 0.13/0.41 fof(f602,plain,(
% 0.13/0.41 ~ssList(nil)|~sQ0_spl|~sQ3_spl),
% 0.13/0.41 inference(resolution,[status(thm)],[f601,f475])).
% 0.13/0.41 fof(f603,plain,(
% 0.13/0.41 ~sQ6_spl|~sQ0_spl|~sQ3_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f602,f504,f438,f448])).
% 0.13/0.41 fof(f609,plain,(
% 0.13/0.41 ~ssList(sK47_skl)|~ssList(nil)|sK47_skl=nil|sQ4_spl),
% 0.13/0.41 inference(resolution,[status(thm)],[f454,f220])).
% 0.13/0.41 fof(f610,definition,(
% 0.13/0.41 sQ19_spl <=> (sK47_skl=nil)),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f611,plain,(
% 0.13/0.41 sK47_skl=nil|~sQ19_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f610])).
% 0.13/0.41 fof(f613,plain,(
% 0.13/0.41 ~sQ7_spl|~sQ6_spl|sQ19_spl|sQ4_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f609,f507,f504,f610,f452])).
% 0.13/0.41 fof(f614,plain,(
% 0.13/0.41 ~frontsegP(sK50_skl,sK47_skl)|sQ5_spl),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f424,f457])).
% 0.13/0.41 fof(f615,plain,(
% 0.13/0.41 $false|sQ1_spl|~sQ19_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f611,f517])).
% 0.13/0.41 fof(f616,plain,(
% 0.13/0.41 sQ1_spl|~sQ19_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f615])).
% 0.13/0.41 fof(f619,plain,(
% 0.13/0.41 ~ssList(sK50_skl)|~ssList(sK47_skl)|frontsegP(app(sK47_skl,sK51_skl),sK47_skl)|~ssList(sK51_skl)),
% 0.13/0.41 inference(paramodulation,[status(thm)],[f500,f463])).
% 0.13/0.41 fof(f620,definition,(
% 0.13/0.41 sQ20_spl <=> (ssList(sK50_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f622,plain,(
% 0.13/0.41 ~ssList(sK50_skl)|sQ20_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f620])).
% 0.13/0.41 fof(f623,plain,(
% 0.13/0.41 ~sQ20_spl|~sQ7_spl|sQ8_spl|~sQ9_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f619,f620,f507,f510,f513])).
% 0.13/0.41 fof(f624,plain,(
% 0.13/0.41 ![X0]: (~ssList(X0)|~ssList(nil)|app(sK6_skl(nil,X0),nil)=X0|~ssList(X0))),
% 0.13/0.41 inference(resolution,[status(thm)],[f129,f309])).
% 0.13/0.41 fof(f626,definition,(
% 0.13/0.41 ![X0]: (sQ21_spl <=> (~ssList(X0)|app(sK6_skl(nil,X0),nil)=X0|~ssList(X0)))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f629,plain,(
% 0.13/0.41 sQ21_spl|~sQ6_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f624,f626,f504])).
% 0.13/0.41 fof(f632,plain,(
% 0.13/0.41 ~ssList(sK50_skl)|~ssList(sK51_skl)|rearsegP(app(sK47_skl,sK51_skl),sK51_skl)|~ssList(sK47_skl)),
% 0.13/0.41 inference(paramodulation,[status(thm)],[f500,f464])).
% 0.13/0.41 fof(f633,definition,(
% 0.13/0.41 sQ22_spl <=> (rearsegP(app(sK47_skl,sK51_skl),sK51_skl))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f634,plain,(
% 0.13/0.41 rearsegP(app(sK47_skl,sK51_skl),sK51_skl)|~sQ22_spl),
% 0.13/0.41 inference(component_clause,[status(thm)],[f633])).
% 0.13/0.41 fof(f636,plain,(
% 0.13/0.41 ~sQ20_spl|~sQ9_spl|sQ22_spl|~sQ7_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f632,f620,f513,f633,f507])).
% 0.13/0.41 fof(f637,plain,(
% 0.13/0.41 $false|sQ20_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f622,f423])).
% 0.13/0.41 fof(f638,plain,(
% 0.13/0.41 sQ20_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f637])).
% 0.13/0.41 fof(f639,plain,(
% 0.13/0.41 rearsegP(sK50_skl,sK51_skl)|~sQ22_spl),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f500,f634])).
% 0.13/0.41 fof(f640,plain,(
% 0.13/0.41 ~ssList(sK50_skl)|~ssList(sK51_skl)|app(sK6_skl(sK51_skl,sK50_skl),sK51_skl)=sK50_skl|~sQ22_spl),
% 0.13/0.41 inference(resolution,[status(thm)],[f639,f129])).
% 0.13/0.41 fof(f641,definition,(
% 0.13/0.41 sQ23_spl <=> (app(sK6_skl(sK51_skl,sK50_skl),sK51_skl)=sK50_skl)),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f644,plain,(
% 0.13/0.41 ~sQ20_spl|~sQ9_spl|sQ23_spl|~sQ22_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f640,f620,f513,f641,f633])).
% 0.13/0.41 fof(f645,plain,(
% 0.13/0.41 frontsegP(sK50_skl,sK47_skl)|~sQ8_spl),
% 0.13/0.41 inference(forward_demodulation,[status(thm)],[f500,f511])).
% 0.13/0.41 fof(f646,plain,(
% 0.13/0.41 $false|sQ5_spl|~sQ8_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f645,f614])).
% 0.13/0.41 fof(f647,plain,(
% 0.13/0.41 sQ5_spl|~sQ8_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f646])).
% 0.13/0.41 fof(f652,plain,(
% 0.13/0.41 sP0_prd(nil,nil)|~sQ19_spl|~sQ2_spl),
% 0.13/0.41 inference(backward_demodulation,[status(thm)],[f611,f522])).
% 0.13/0.41 fof(f658,plain,(
% 0.13/0.41 $false|~sQ19_spl|~sQ2_spl),
% 0.13/0.41 inference(forward_subsumption_resolution,[status(thm)],[f652,f489])).
% 0.13/0.41 fof(f659,plain,(
% 0.13/0.41 ~sQ19_spl|~sQ2_spl),
% 0.13/0.41 inference(contradiction_clause,[status(thm)],[f658])).
% 0.13/0.41 fof(f674,plain,(
% 0.13/0.41 ![X0]: (~ssList(X0)|~ssList(nil)|app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0))=X0|~ssList(X0))),
% 0.13/0.41 inference(resolution,[status(thm)],[f136,f323])).
% 0.13/0.41 fof(f676,definition,(
% 0.13/0.41 ![X0]: (sQ24_spl <=> (~ssList(X0)|app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0))=X0|~ssList(X0)))),
% 0.13/0.41 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.13/0.41 fof(f679,plain,(
% 0.13/0.41 sQ24_spl|~sQ6_spl),
% 0.13/0.41 inference(split_clause,[status(thm)],[f674,f676,f504])).
% 0.13/0.41 fof(f700,plain,(
% 0.13/0.41 app(nil,sK47_skl)=sK47_skl),
% 0.13/0.41 inference(resolution,[status(thm)],[f249,f420])).
% 0.13/0.41 fof(f706,plain,(
% 0.13/0.41 app(nil,sK51_skl)=sK51_skl),
% 0.13/0.41 inference(resolution,[status(thm)],[f249,f426])).
% 0.13/0.41 fof(f707,plain,(
% 0.13/0.41 app(nil,nil)=nil),
% 0.13/0.41 inference(resolution,[status(thm)],[f249,f223])).
% 0.13/0.41 fof(f729,plain,(
% 0.13/0.41 app(sK47_skl,nil)=sK47_skl),
% 0.13/0.41 inference(resolution,[status(thm)],[f389,f420])).
% 0.13/0.41 fof(f735,plain,(
% 0.13/0.41 app(sK51_skl,nil)=sK51_skl),
% 0.13/0.41 inference(resolution,[status(thm)],[f389,f426])).
% 0.13/0.41 fof(f753,plain,(
% 0.13/0.41 ![X0]: (~ssList(app(sK51_skl,X0))|~ssList(nil)|segmentP(app(app(sK51_skl,nil),X0),nil)|~ssList(sK51_skl)|~ssList(X0))),
% 0.13/0.42 inference(paramodulation,[status(thm)],[f735,f465])).
% 0.13/0.42 fof(f754,plain,(
% 0.13/0.42 ![X0]: (~ssList(app(nil,X0))|~ssList(nil)|segmentP(app(app(nil,nil),X0),nil)|~ssList(nil)|~ssList(X0))),
% 0.13/0.42 inference(paramodulation,[status(thm)],[f707,f465])).
% 0.13/0.42 fof(f755,plain,(
% 0.13/0.42 ![X0]: (~ssList(app(sK51_skl,X0))|~ssList(sK51_skl)|segmentP(app(app(nil,sK51_skl),X0),sK51_skl)|~ssList(nil)|~ssList(X0))),
% 0.13/0.42 inference(paramodulation,[status(thm)],[f706,f465])).
% 0.13/0.42 fof(f756,plain,(
% 0.13/0.42 ![X0]: (~ssList(app(sK47_skl,X0))|~ssList(sK47_skl)|segmentP(app(app(nil,sK47_skl),X0),sK47_skl)|~ssList(nil)|~ssList(X0))),
% 0.13/0.42 inference(paramodulation,[status(thm)],[f700,f465])).
% 0.13/0.42 fof(f757,plain,(
% 0.13/0.42 ![X0]: (~ssList(app(sK47_skl,X0))|~ssList(nil)|segmentP(app(app(sK47_skl,nil),X0),nil)|~ssList(sK47_skl)|~ssList(X0))),
% 0.13/0.42 inference(paramodulation,[status(thm)],[f729,f465])).
% 0.13/0.42 fof(f761,definition,(
% 0.13/0.42 ![X0]: (sQ26_spl <=> (~ssList(app(sK51_skl,X0))|segmentP(app(app(sK51_skl,nil),X0),nil)|~ssList(X0)))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f764,plain,(
% 0.13/0.42 sQ26_spl|~sQ6_spl|~sQ9_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f753,f761,f504,f513])).
% 0.13/0.42 fof(f765,definition,(
% 0.13/0.42 ![X0]: (sQ27_spl <=> (~ssList(app(nil,X0))|segmentP(app(app(nil,nil),X0),nil)|~ssList(X0)))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f768,plain,(
% 0.13/0.42 sQ27_spl|~sQ6_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f754,f765,f504])).
% 0.13/0.42 fof(f769,definition,(
% 0.13/0.42 ![X0]: (sQ28_spl <=> (~ssList(app(sK51_skl,X0))|segmentP(app(app(nil,sK51_skl),X0),sK51_skl)|~ssList(X0)))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f772,plain,(
% 0.13/0.42 sQ28_spl|~sQ9_spl|~sQ6_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f755,f769,f513,f504])).
% 0.13/0.42 fof(f773,definition,(
% 0.13/0.42 ![X0]: (sQ29_spl <=> (~ssList(app(sK47_skl,X0))|segmentP(app(app(nil,sK47_skl),X0),sK47_skl)|~ssList(X0)))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f776,plain,(
% 0.13/0.42 sQ29_spl|~sQ7_spl|~sQ6_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f756,f773,f507,f504])).
% 0.13/0.42 fof(f777,definition,(
% 0.13/0.42 ![X0]: (sQ30_spl <=> (~ssList(app(sK47_skl,X0))|segmentP(app(app(sK47_skl,nil),X0),nil)|~ssList(X0)))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f780,plain,(
% 0.13/0.42 sQ30_spl|~sQ6_spl|~sQ7_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f757,f777,f504,f507])).
% 0.13/0.42 fof(f928,plain,(
% 0.13/0.42 ~ssList(sK47_skl)|~ssList(nil)|~frontsegP(sK47_skl,nil)|sK47_skl=nil|~sQ2_spl|~sQ8_spl),
% 0.13/0.42 inference(resolution,[status(thm)],[f284,f593])).
% 0.13/0.42 fof(f929,plain,(
% 0.13/0.42 ![X0]: (~ssList(nil)|~ssList(X0)|~frontsegP(nil,X0)|nil=X0|~ssList(X0))),
% 0.13/0.42 inference(resolution,[status(thm)],[f284,f295])).
% 0.13/0.42 fof(f932,definition,(
% 0.13/0.42 sQ45_spl <=> (frontsegP(sK47_skl,nil))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f934,plain,(
% 0.13/0.42 ~frontsegP(sK47_skl,nil)|sQ45_spl),
% 0.13/0.42 inference(component_clause,[status(thm)],[f932])).
% 0.13/0.42 fof(f935,plain,(
% 0.13/0.42 ~sQ7_spl|~sQ6_spl|~sQ45_spl|sQ19_spl|~sQ2_spl|~sQ8_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f928,f507,f504,f932,f610,f445,f510])).
% 0.13/0.42 fof(f936,definition,(
% 0.13/0.42 ![X0]: (sQ46_spl <=> (~ssList(X0)|~frontsegP(nil,X0)|nil=X0|~ssList(X0)))),
% 0.13/0.42 introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition])).
% 0.13/0.42 fof(f939,plain,(
% 0.13/0.42 ~sQ6_spl|sQ46_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f929,f504,f936])).
% 0.13/0.42 fof(f942,plain,(
% 0.13/0.42 ~ssList(sK47_skl)|sQ45_spl),
% 0.13/0.42 inference(resolution,[status(thm)],[f934,f295])).
% 0.13/0.42 fof(f944,plain,(
% 0.13/0.42 ~sQ7_spl|sQ45_spl),
% 0.13/0.42 inference(split_clause,[status(thm)],[f942,f507,f932])).
% 0.13/0.42 fof(f949,plain,(
% 0.13/0.42 $false),
% 0.13/0.42 inference(sat_refutation,[status(thm)],[f444,f451,f458,f519,f573,f575,f578,f584,f603,f613,f616,f623,f629,f636,f638,f644,f647,f659,f679,f764,f768,f772,f776,f780,f935,f939,f944])).
% 0.13/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.43 % Elapsed time: 0.077601 seconds
% 0.13/0.43 % CPU time: 0.330486 seconds
% 0.13/0.43 % Total memory used: 113.894 MB
% 0.13/0.43 % Net memory used: 113.532 MB
%------------------------------------------------------------------------------